'To feel defensive' is to feel protective or defensive of something.

'To feel strangely defensive' is to feel this but for an unknown reason or a larger amount than expected.

E.g. When I read this I felt strangely defensive of modern communication [because I'm surprisingly proud of modern communication as it's a part of me, and so reading criticism makes me feel strangely defensive], for example.

Obviously haven't read the article so I can't say that's what the author was saying, but I hope this helps in understanding the phrase!